Q. No.Three particles are moving with constant velocities \(v_1 ,v_2\) and \(v\) respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among \(v_1 ,v_2\) and \(v\) is:
1. \(v =v_1+v_2\)
2. \(v= \sqrt{v_{1} v_{2}}\)
3. \(v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}\)
1. \(v =v_1+v_2\)
2. \(v= \sqrt{v_{1} v_{2}}\)
3. \(v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}\)
A body is thrown horizontally with a velocity from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is:
(1) h
(2)
(3) 2h
(4)
A particle starts from the origin at t=0 and moves in the x-y plane with a constant acceleration 'a' in the y direction. Its equation of motion is . The x component of its velocity (at t=0) will be:
1. variable
2.
3.
4.
A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is :
(1) 10 km/hr
(2) 8 km/hr
(3) 6 km/hr
(4) 4 km/hr
A boat moves with a speed of \(5\) km/h relative to water in a river flowing with a speed of \(3\) km/h. Width of the river is \(1\) km. The minimum time taken for a round trip will be:
1. \(5\) min
2. \(60\) min
3. \(20\) min
4. \(30\) min
A river is flowing from \(W\) to \(E\) with a speed of \(5\) m/min. A man can swim in still water with a velocity of \(10\) m/min. In which direction should the man swim so as to take the shortest possible path to go to the south:
| 1. | \(30^{\circ}\) with downstream |
| 2. | \(60^{\circ}\) with downstream |
| 3. | \(120^{\circ}\) with downstream |
| 4. | South |
If a particle moves in a circle describing equal angles in equal times, its velocity vector:
(1) remains constant.
(2) changes in magnitude.
(3) changes in direction.
(4) changes both in magnitude and direction.
A motorcyclist going round in a circular track at constant speed has:
(1) constant linear velocity
(2) constant acceleration
(3) constant angular velocity
(4) constant force
A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B, the angular velocity of P about A and C are in the ratio
(1) 1 : 1
(2) 1 : 2
(3) 2 : 1
(4) 4 : 1
The angular speed of a fly wheel making \(120\) revolutions/minute is:
1. \(2\pi~\mathrm{rad/s}\)
2. \(4\pi^2~\mathrm{rad/s}\)
3. \(\pi~\mathrm{rad/s}\)
4. \(4\pi~\mathrm{rad/s}\)
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